Finite Group Databasebeta

C2×C4×Dic1094 #46855466

order35008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C4×Dic1094

Splittings

SylowC547 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22×C4C2×D547
commutatorC2×C547C23×C4
FrattiniC22C23×D547
FittingC2×C42×C547C2
socle, prime radicalC23×C547C23
cosocleC22×C547C24
hypercenterC2×C42D547
hypocenterC547C2×C4×Q8
LCSG ▷ C2×C547 ▷ C547
UCSC1 ◁ C22×C4 ◁ C2×C42

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 35008

Conjugacy classes & character table

8776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35008, 1014);